Tracking Equivalent Mechanistic Interpretations Across Neural Networks

arXiv cs.CL / 4/1/2026

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Key Points

The paper studies scalable mechanistic interpretability by formalizing “interpretive equivalence,” i.e., when two models share a common interpretation without explicitly stating what it is.
It proposes a core equivalence principle: two interpretations are equivalent if all possible implementations of them are also equivalent.
The authors develop an algorithm to estimate interpretive equivalence and demonstrate it via case studies on Transformer-based models.
To support analysis, they derive necessary and sufficient conditions for interpretive equivalence using representation similarity and provide guarantees linking algorithmic interpretations, circuits, and representations.
The framework is intended to enable more rigorous evaluation of mechanistic interpretability and to support automated, generalizable interpretation discovery methods.

Abstract

Mechanistic interpretability (MI) is an emerging framework for interpreting neural networks. Given a task and model, MI aims to discover a succinct algorithmic process, an interpretation, that explains the model's decision process on that task. However, MI is difficult to scale and generalize. This stems in part from two key challenges: there is no precise notion of a valid interpretation; and, generating interpretations is often an ad hoc process. In this paper, we address these challenges by defining and studying the problem of interpretive equivalence: determining whether two different models share a common interpretation, without requiring an explicit description of what that interpretation is. At the core of our approach, we propose and formalize the principle that two interpretations of a model are equivalent if all of their possible implementations are also equivalent. We develop an algorithm to estimate interpretive equivalence and case study its use on Transformer-based models. To analyze our algorithm, we introduce necessary and sufficient conditions for interpretive equivalence based on models' representation similarity. We provide guarantees that simultaneously relate a model's algorithmic interpretations, circuits, and representations. Our framework lays a foundation for the development of more rigorous evaluation methods of MI and automated, generalizable interpretation discovery methods.